Toss peach halves with brown sugar and lemon juice, and place them cut-side-up on the prepared baking sheet. Roast until the peaches are tender, 20 to 30 minutes. If the juice on the pan begins to burn, add a little water and loosely cover the fruit with foil.

Top each peach half with a 1/2-cup scoop of frozen yogurt and a sprinkle of crumbled gingersnaps (if using). Serve immediately.